A beam carring a uniform load is simply supported with thesupports set back a di

Question

A beam carring a uniform load is simply supported with thesupports set back a distance "a" from the ends. The designer wishesto minimize the neccessary weight of the supporting beam bychoosing a setback distance "a" resulting in the smallest possiblebending stress. Beam length is "L" The set back distance "a" is the same for both ends. Max positive moment is at L/2 Max negative moment is at the supports. When Max positive moment = max neg moment what is "a"? if w = 100 lb/in and "L"= 10" what is the max moment? Answers were given as "a" = 0.207L and M= 214 lb in. Can somebody help me derive the general equations to get theseanswers?

Explanation / Answer

correction "a" = 0.207L

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